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56 votes
21 answers
18k views

Wonderful applications of the Vandermonde determinant

This semester I am assisting my mentor teaching a first-year undergraduate course on linear algebra in Peking University, China. And now we have come to the famous Vandermonde determinant, which has ...
19 votes
17 answers
7k views

Vector spaces without natural bases

Does anyone know any nice examples of vector spaces without a basis that is in some sense "natural". To clarify what I mean, suppose we look at $\mathbb{R}^2$. We define $\mathbb{R}^2$ as pairs of ...